Human neural stem cells (NSCs), modified to express a therapeutic transgene, may hold promise for brain tumor therapy due to their inherent tumor-tropic properties and potential use as vehicles for delivering chemotherapy directly to infiltrating glioma cells in the brain. NSCs ca overcome obstacles of drug-delivery that limit current gene therapy strategies to provide an effective anti-tumor response. Data from animal models have demonstrated the safety and efficacy of NSCs for tracking to invasive tumor cells as well as to distant micro-tumor foci and delivering therapeutic gene products to tumor cells. The investigators have recently completed a first-in-human pilot study of cytosine deaminase (CD)-expressing NSCs given in combination with oral 5-fluorocytosine (5-FC), demonstrating that one dose of NSCs followed by a 7-day course of 5-FC in recurrent high-grade glioma patients was safe and feasible. With intracerebral microdialysis, the investigators reported that they documented proof-of-concept-that the NSCs convert the prodrug 5-FC to its active metabolite 5-FU in the brain. It was reported that results of immunologic correlative studies showed no evidence of NSC immunogenicity after first exposure. Autopsy data provided evidence that NSCs migrated to distant tumor sites and did not divide and form secondary tumors. The investigators propose that the next step in the clinical development of this new treatment strategy for gliomas is to perform a Phase 1 trial to assess the feasibility of intracranially administering repeat doses of these allogeneic NSCs while continuing to dose escalate to determine the Phase 2 recommended doses of study treatment. Leucovorin, which enhances the efficacy of 5-FU and can cross the blood-brain barrier, will be added to the treatment regimen once the MTD for the combination of NSCs and 5-FC has been identified. The investigators will continue to monitor patients for possible development of immune reactivity against NSCs, study the distribution NSCs on MRI by iron-labeling the NSCs, and measure NSC conversion of 5-FC to 5-FU via intracerebral microdialysis at the MTD of study treatment. In anticipation of performing larger efficacy studies of this treatment strategy at multiple cancer centers, this proposed single center Phase 1 study will assess the feasibility of recently optimized NSC manufacturing and final preparation standard operating procedures. The investigators propose that establishing a simplified process for final NSC preparation before administering to a patient will enable the NSCs to be distributed and easily used at other treatment sites in future multi-center NSC trials.